When starting an aircraft engine such as a gas turbine engine, it is desirable to use an electric starter operating at the highest optimum speed since the starter motor can then have a smaller and a lighter construction compared to a motor operating at a lower rotation speed. However, when the engine is running, the operating speed of the engine can be many times the starting speed and a smaller-sized starter may need to be disconnected from the engine to prevent it from overspeeding. If the electrical machine remains continuously connected to the engine spool shaft, concessions in machine design need to be made in order to allow a sufficiently robust machine to operate in both starting and generating conditions, which results in associated weight penalties. Room for improvement thus exists.